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Mirrors > Home > ILE Home > Th. List > ralrnmpo | Unicode version |
Description: A restricted quantifier over an image set. (Contributed by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
rngop.1 | |
ralrnmpo.2 |
Ref | Expression |
---|---|
ralrnmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rngop.1 | . . . . 5 | |
2 | 1 | rnmpo 5963 | . . . 4 |
3 | 2 | raleqi 2669 | . . 3 |
4 | eqeq1 2177 | . . . . 5 | |
5 | 4 | 2rexbidv 2495 | . . . 4 |
6 | 5 | ralab 2890 | . . 3 |
7 | ralcom4 2752 | . . . 4 | |
8 | r19.23v 2579 | . . . . 5 | |
9 | 8 | albii 1463 | . . . 4 |
10 | 7, 9 | bitr2i 184 | . . 3 |
11 | 3, 6, 10 | 3bitri 205 | . 2 |
12 | ralcom4 2752 | . . . . . 6 | |
13 | r19.23v 2579 | . . . . . . 7 | |
14 | 13 | albii 1463 | . . . . . 6 |
15 | 12, 14 | bitri 183 | . . . . 5 |
16 | nfv 1521 | . . . . . . . 8 | |
17 | ralrnmpo.2 | . . . . . . . 8 | |
18 | 16, 17 | ceqsalg 2758 | . . . . . . 7 |
19 | 18 | ralimi 2533 | . . . . . 6 |
20 | ralbi 2602 | . . . . . 6 | |
21 | 19, 20 | syl 14 | . . . . 5 |
22 | 15, 21 | bitr3id 193 | . . . 4 |
23 | 22 | ralimi 2533 | . . 3 |
24 | ralbi 2602 | . . 3 | |
25 | 23, 24 | syl 14 | . 2 |
26 | 11, 25 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1346 wceq 1348 wcel 2141 cab 2156 wral 2448 wrex 2449 crn 4612 cmpo 5855 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-cnv 4619 df-dm 4621 df-rn 4622 df-oprab 5857 df-mpo 5858 |
This theorem is referenced by: txcnp 13065 txcnmpt 13067 |
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